SUBJECT 25832 - Statistics and Data Analysis COMPETENCIAS

321 - Faculty of Economics and Business Studies
GADEMP30 - Bachelor`s Degree in Business Administration and Management Curso
Second year
Créditos ECTS : 6
25832 - Statistics and Data Analysis
Lay the foundations of Descriptive Statistics and Probability Theory both from a theoretical and applied point of view.
Initiate the student in the Probability Calculus, useful for a latter design and analysis of theoretical statistical models, which
will act as a link between the data observed in a sample and what is unknown in the population. Probability will be
presented as an uncertainty measure. An appropriate methodology will be developed in order to extend the analysis of the
probabilities of some simple results obtained from a random experiment. These methods are based on mathematical
techniques and are themselves the basis of the procedures to be developed in other Statistics subjects to be taken in
further courses.
I Descriptive statistics
1. Univariate statistical variables: plots and summary statistics.
Univariate statistical variables. Frequency distributions. Bar charts. Histogram. Frequency polygon. Pie chart. Simple and
weighted arithmetic mean. Median and quantiles. Mode. Variance. Standard deviation. Coefficient of variation. Range and
mean deviation. Box plot. Skewness. Kurtosis. Gini index. Lorenz curve. Centered and standardized variables. Effect of
linear transformations.
2. Bivariate statistical variables: plots and summary statistics.
Bivariate statistical variables. Frequency distributions. Marginal distributions. Conditional distributions. Scatter plot.
Covariance. Correlation coefficient. Statistics for linear combinations of statistical variables.
3. Index numbers.
Simple index numbers: properties. Average cumulative rate. Unweighted complex indices: simple arithmetic mean and
simple aggregative mean. Weighted complex indices: Laspeyres, Paasche, Fisher indices. Changes in the base period.
Deflation of statistical series: current and constant values. Applications.
II Probability
4. Principles of probability.
Introduction. Axioms. Probability allocation. Probabilities as relative frequencies. Stochastic independence. Conditional
probability. Intersection theorem. Partition theorem. Bayes theorem.
5. Random variable. Probability distribution. Probability distributions and transformations of random variables.
Random variable in R. Distribution function in R. Discrete and continuous random variables. Probability mass functions
and density functions. Examples of discrete and continuous probability distributions: Bernoulli, binomial, uniform and
exponential. Transformations in R and R². Random variable in R2. Distribution function in R2. Marginal distributions.
Conditioned distributions. Stochastic independence.
6. Mathematical expectation, moments, characteristic function.
Mathematical expectation of a function in R. Moments in R. Chebyschev's inequality. Characteristic, moment generating
and cumulant generating functions. Mathematical expectation in R². Covariance. Correlation coefficient. Correlation and
independence. Conditional expectation.
Página :
7. Normal distribution. Central limit theorem.
Definition and basic properties of the N(0,1) distribution. Linear transformations. General normal distribution. Linear
combination of independent normally distributed variables. Sequence of random variables. Definition of convergence in
law. Continuity theorem of characteristic functions. Asymptotic normal distributions. Central limit theorem.
Tipo de Docencia
Horas de Docencia Presencial
Horas de Actividad No Presencial del Alumno
M: Magistral
S: Seminario
GA: P. de Aula
GL: P. Laboratorio
GCL: P. Clínicas
TA: Taller
TI: Taller Ind.
GCA: P. de Campo
GO: P. Ordenador
Aclaraciones :
Teaching will be based upon formal lectures, practical lectures and seminars. Some seminars may take place at the
computer room.
Formal lectures will be about the theoretical contents of the subject. The applied lectures will include exercise solving and
examples illustrative of the theory.
- Examen escrito a desarrollar
- Examen escrito tipo test
- Realización de prácticas (ejercicios, casos o problemas)
- Trabajos individuales
Aclaraciones :
1st exam round (January)
The student will choose one out of the two following evaluation systems:
1. A mixed evaluation based on exercises tried during the coursework and a written final examination. The final exam will
account for 70% of the full final qualification and the evaluation of coursework exercises (otherwise known as continuous
evaluation) will account for the remaining 30%. However, the student must obtain at least 4 points out of 10 in the Final
exam in order to get the marks from the continuous evaluation added to the final qualification. That is, any student not
achieving at least 4 points in the Final exam alone, will get a Fail as his/her final qualification, whatever the marks from the
continuous evaluation.
2. A full final examination for 100% of the final qualification.
Any student willing to choose the second system, and who will have his/her qualification drawn from the Final exam alone
(100%), must apply for it in a written form which can be obtained from the teacher and return it to the teacher within the
first four weeks of the course. Failure to do so implies that the student chooses the mixed evaluation system.
Any student not present in the Final exam official date and place will get an absent (No presentado) as qualification,
whatever election of evaluation system.
2nd exam round (June)
The qualification will be obtained solely (100%) from the corresponding Final examination, to be celebrated at the official
date and place.
Página :
Bibliografía básica
Basic reading:
1. M.J. Bárcena, K. Fernández, E. Ferreira and M.A. Garín (2003). Estadística Descriptiva. Servicio Editorial de la
Universidad del País Vasco, UPV/EHU.
2. F.J. Martín Pliego and L. Ruiz Maya (2004). Estadística I: Probabilidad. Editorial AC, 2ª edición. Madrid.
3. D. Peña (2001). Fundamentos de Estadística. Alianza Editorial, Madrid.
4. D. Peña and J. Romo, J. (1997). Introducción a la Estadística para las Ciencias Sociales. McGraw Hill,
5. S. Ross (2001). Probability and Statistics for Engineers and Scientists. Academic Press, London.
6. E. Paradis (2003). R for beginners. Institut des Sciences de l'Evolution. Université Montpellier II, France. (
7. Ross, S. (2010). A first course in Probability, 6th edition. Pearson.
1. J. Arteche et al. (2000). Ejercicios de Estadística I. Elementos de Probabilidad y Estadística. Servicio Editorial de
2. F.J. Martín Pliego, J.M. Montero Lorenzo and F.J. Ruiz Maya (2002). Problemas de Probabilidad. Editorial AC,
3. F. Tusell and M.A. Garín (1991). Ejercicios de Probabilidad e Inferencia Estadística. Tébar-Flores, Madrid.
Bibliografía de profundización
1. Grimmett, G. and Welsh, D. (1991). Probability: an introduction. Oxford.
2. Grinstead, C.M. and Snell, J.L. (-). Introduction to Probability.
3. Lind, D.A. (1994). Basic statistics for Business and Economics. Irwin.
4. Newbold, P. (2003). Statistics for Business and Economics. Prentice Hall.
5. MacClave, J.T. (1994). Statistics for Business and Economics. MacMillan.
6. MacClave, J. T. (2001). A first course in business statistics, Prentice Hall.
7. Levin, S. and Rubin, S. (1994). Statistics for Management. Prentice Hall.
Direcciones de internet de interés
The University of the Basque Country (UPV-EHU) has appointed for agreements with some publishers so that students
can download freely books in PDF format for their personal use. More information in
Página :